Michael:

That the path leading to any node is distinct, is already built into the definition. To see this, note that, by definition, each node IS a path, i.e. a sequence of actions (a0,a1,a2,...,ak). Hence, the MEANING of the statement "(a0,a1,a2,...,ak) is a path leading to x0" is precisely that x0=(a0,a1,a2,...,ak). Consequently, if two paths lead to the single node x0, these two paths must be identical. That is, each node has a unique path leading to it.


Phil Reny